Personally I doubt it would be possible to stop any contact with the Americas before they develop to an extent that they wouldn't be threatened by Europeans/Japanese/Arabs/whoever the hell else, but it would be possible to keep them isolated for a few more decades, hopefully allowing the emergence of a stronger, more advanced and more stable Pan-Meso-American cultural grouping, encompassing the Taino.
This would most likely be via some butterflying keeping the centre of European power in the east, in Austria-Hungary and Bohemia's area. This would reduce the seafaring tradition, and Spain, Portugal, France and Britain wouldn't be able to fund all these naval expeditions. They might well be pushed back further by the Muslims in the West due to this reduced power. Nevertheless, the trade route problem would still be a big deal, so unless they trade through Slavic lands in OTL Russia, then they're gonna have to deal with the Muslims. But whatever happens, Europe's gaze stays fixed inwards.
Eventually, either the Muslims or the Europeans, in some mad venture, perhaps still looking for trade routes, would reach the Americas. Or, depending how long we leave it, maybe a West African megacultural region or something like that would do it. But someone in western Afro-Eurasia would get there, and then you're on your way. I don't see it happening with the Asians, although Chinese/Japanese/Korean/Vietnamese naval missions going up north to the Chukchis and so on for whatever reason might discover Alaska, and if they begin trading there, or get swept off course enough, they might realise that this is an entirely new land.
Hopefully by this point Mesoamerica will be more developed, and a few states will survive in some form, to declare independence from the colonial empires later with indigenous majorities and native cultures, comparable to the OTL Morocco/Tunisia situation.